Computational Methods in Transport: Granlibakken

Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.

Table of Contents:
Astrophysics.- Radiation Hydrodynamics in Astrophysics.- Radiative Transfer in Astrophysical Applications.- Neutrino Transport in Core Collapse Supernovae.- Discrete-Ordinates Methods for Radiative Transfer in the Non-Relativistic Stellar Regime.- Atmospheric Science, Oceanography, and Plant Canopies.- Effective Propagation Kernels in Structured Media with Broad Spatial Correlations, Illustration with Large-Scale Transport of Solar Photons Through Cloudy Atmospheres.- Mathematical Simulation of the Radiative Transfer in Statistically Inhomogeneous Clouds.- Transport Theory for Optical Oceanography.- Perturbation Technique in 3D Cloud Optics: Theory and Results.- Vegetation Canopy Reflectance Modeling with Turbid Medium Radiative Transfer.- Rayspread: A Virtual Laboratory for Rapid BRF Simulations Over 3-D Plant Canopies.- High Energy Density Physics.- Use of the Space Adaptive Algorithm to Solve 2D Problems of Photon Transport and Interaction with Medium.- Accurate and Efficient Radiation Transport in Optically Thick Media - by Means of the Symbolic Implicit Monte Carlo Method in the Difference Formulation.- An Evaluation of the Difference Formulation for Photon Transport in a Two Level System.- Non-LTE Radiation Transport in High Radiation Plasmas.- Finite-Difference Methods Implemented in SATURN Complex to Solve Multidimensional Time-Dependent Transport Problems.- Implicit Solution of Non-Equilibrium Radiation Diffusion Including Reactive Heating Source in Material Energy Equation.- Mathematics and Computer Science.- Transport Approximations in Partially Diffusive Media.- High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation.- Obtaining Identical Results on Varying Numbers of Processors in Domain Decomposed Particle Monte Carlo Simulations.- KM-Method of Iteration Convergence Acceleration for Solving a 2D Time-Dependent Multiple-Group Transport Equation and its Modifications.- A Regularized Boltzmann Scattering Operator for Highly Forward Peaked Scattering.- Implicit Riemann Solvers for the Pn Equations.- The Solution of the Time-Dependent SN Equations on Parallel Architectures.- Different Algorithms of 2D Transport Equation Parallelization on Random Non-Orthogonal Grids.- Neutron Transport.- Parallel Deterministic Neutron Transport with AMR.- An Overview of Neutron Transport Problems and Simulation Techniques.